A vehicle equipped with an automatic transmission of the type including a hydrodynamic power transmission, such as a torque converter or a fluid coupling, frequently encounters a problem called "creeping phenomenon" which permits gradual movement of the vehicle from its standstill state. To obviate this problem, an automatic transmission has been proposed which is automatically placed in its neutral mode when the vehicle is in a state of standstill and the accelerator pedal has not been depressed. As soon as depression of the accelerator pedal is detected, frictional engaging devices such as brakes and clutches are selectively engaged to attain power transmission.
Vibration of the engine and fuel consumption of the engine in a standstill state of the vehicle can be reduced by employment of the automatic transmission of the above construction. However, there occurs a substantial shock at the time of vehicle starting due to abrupt engagement of the frictional engaging devices.
This problem can be obviated by gradually engaging the frictional engaging devices at the time of vehicle starting. However, such gradual engagement of the frictional engaging devices leads to further problems in that establishment of the power transmission system at the time of vehicle starting time is delayed, this resulting in degradation of the starting acceleration characteristic. Also, a rise in the engine rotation speed can impart excessive load to the frictional engaging devices and result in burnout of the frictional engaging devices.